Page:Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt.pdf/6

One recognizes that this formula is the same as the one that was derived from Maxwell theory and electron theory. Equating the coefficients of the formula's:

${\frac {R}{N}}{\frac {8\pi }{L^{3}}}={\frac {\alpha }{\beta }}$

or

$N={\frac {\beta }{\alpha }}{\frac {8\pi R}{L^{3}}}=6.17\cdot 10^{23},$

that is, a hydrogen atom weighs 1/N gram = 1.62·10^-24g. This is precisely the value found by Mr. Planck, which is in satisfactory agreement with values obtained in other ways.

This brings us to the conclusion: the larger the energy density and the wavelength of radiation the more suitable the theoretical basis that we used; but for small wavelengths and low radiation densities the basis fails completely.

In the following the "black body radiation" is to be considered in terms of what is experienced, without forming a picture of the creation and propagation of the radiation.

The Entropy of Radiation

The following discussion is contained in a famous work of Mr. Wien, and is only included here for the sake of completeness.

Let there be radiation taking up volume v. We assume that the observable properties of the radiation are determined completely when the radiation densities ρ(ν) are given for all frequencies. ^[1] Since we can regard radiations of different frequency as separable without doing work or transferring heat the entropy of the radiation can be expressed in the form

$S=v\int \limits _{0}^{\infty }\phi (\rho ,\nu )d\nu$

where φ is a function of the variables ρ and ν.

1. This is an arbitrary assumption. The natural course of action is to stay with this simplest assumption until experiment forces us to abandon it.